自激励广义二项门限自回归模型的统计推断  

Statistical Inference for Self-exciting Generalized Binomial Threshold Autoregressive Model

作　　者：张洁 张玉 董小刚 ZHANG Jie;ZHANG Yu;DONG Xiaogang(School of Mathematics and Statistics,Changchun University of Technology,Changchun 130012,China)

机构地区：[1]长春工业大学数学与统计学院,长春130012

出　　处：《吉林大学学报（理学版）》2023年第2期275-284,共10页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11901053);吉林省自然科学基金(批准号:YDZJ202301ZYTS384);吉林省教育厅科学技术研究项目(批准号:JJKH20220671KJ).

摘　　要：针对有上限且数据之间具有相依结构的非线性整数值时间序列数据的建模问题,提出一个自激励广义二项门限自回归模型.首先,证明该模型的严平稳遍历性,并讨论模型的一些统计性质:期望、方差、自协方差和转移概率;其次,分别给出门限变量在已知和未知两种情形下模型参数的条件最大似然估计方法;最后,将该模型应用到一组实际数据中进行拟合验证.Aiming at the modeling problem of nonlinear integer-valued time series data with upper limit and dependent structure between data,we proposed a self-exciting generalized binomial threshold autoregressive model.Firstly,we proved the strictly stationary and ergodicity of the model,and discussed some statistical properties of the model,including the expectation,variance,aoto-covariance and the transition probability.Secondly,we gave the conditional maximum likelihood estimation method of the model parameters in the case of known and unknown threshold variable.Finally,we applied the model to a set of real data for fitting verification.

关 键 词：整数值时间序列 广义二项稀疏算子 门限自回归过程 条件最大似然估计 

分 类 号：O212.1[理学—概率论与数理统计]